Journal Article

Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain

Kulkarni, Manas, Damle, Kedar, Mendl, Christian B., Huse, David A., Dhar, Abhishek, Das, Avijit, Spohn, Herbert

2020

Overview

Using the framework of nonlinear fluctuating hydrodynamics (NFH), we examine equilibrium spatio-temporal correlations in classical ferromagnetic spin chains with nearest neighbor interactions. In particular, we consider the classical XXZ-Heisenberg spin chain (also known as Lattice Landau–Lifshitz or LLL model) evolving deterministically and chaotically via Hamiltonian dynamics, for which energy and z -magnetization are the only locally conserved fields. For the easy-plane case, this system has a low-temperature regime in which the difference between neighboring spin’s angular orientations in the XY plane is an almost conserved field. According to the predictions of NFH, the dynamic correlations in this regime exhibit a heat peak and propagating sound peaks, all with anomalous broadening. We present a detailed molecular dynamics test of these predictions and find a reasonably accurate verification. We find that, in a suitable intermediate temperature regime, the system shows two sound peaks with Kardar-Parisi-Zhang (KPZ) scaling and a heat peak where the expected anomalous broadening is less clear. In high temperature regimes of both easy plane and easy axis case of LLL, our numerics show clear diffusive spin and energy peaks and absence of any sound modes, as one would expect. We also simulate an integrable version of the XXZ-model, for which the ballistic component instead moves with a broad range of speeds rather than being concentrated in narrower peaks around the sound speed.

• Publisher: Springer US,Springer,Springer Nature B.V
• Subject: Analysis / Chains / Computational fluid dynamics / Computer simulation / Ferromagnetism / Fluid dynamics / Fluid flow / Fluid mechanics / High temperature / Hydrodynamics / Lattice vibration / Low temperature / Magnetization / Mathematical and Computational Physics / Molecular dynamics / Physical Chemistry / Physics / Physics and Astronomy / Quantum Physics / Sound / Sound propagation / Statistical Physics and Dynamical Systems / Theoretical